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https://setwithfriends.com/

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Set with Friends * Free, Real-Time Multiplayer Game

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An online card game testing reaction speed and pattern matching abilities. Play by yourself, or compete with your friends in real time!

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We need help to keep Puzzle of the Week running! Please consider donating through our Patreon page or volunteering some time and joining the team. See the Donate page for more information.

Puzzle of the Week is a free international puzzle competition for schools. Students submit answers to a puzzle which is published weekly on Mondays. School and student performances are recorded and leaderboards are published on the results page. You can sign your school up for free using the button above or by clicking here.

All previous puzzles are available with detailed answers including extensions and background information on the puzzle library page.

All Time School Leaderboard
This shows the top 20 schools in the competition since its inception in 2016.

The leaderboard updates live as entries are submitted, just refresh the page to see the most recent data.

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We need help to keep Puzzle of the Week running! Please consider donating through our Patreon page or volunteering some time and joining the team. See the Donate page for more information. Puzzle of the Week is a free international puzzle competition for schools. Students submit answers to a puzzle which is published weekly on Mondays.

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Don't like plant-based meat alternatives, but want to spare animals and the environment? There's hope on the horizon, aided by a good helping of maths.

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Curriculum mapping

A list of Maths Items of the Month categorised by GCSE/A level topics can be seen at: Maths Items of the Month Curriculum mapping.

Recent Maths Items of the Month

September 2019
Midpoints of the intersection of a line and a parabola

M is the midpoint of the points of intersection of y= x ² and y=2 x+ c (as c varies). Why does M move as it does?

July 2019
Sums of three cubes

Both 11 and 12 can be written as the sum of the cubes of three integers:
11 &equals; 3 ³ &plus; (−2) ³ &plus; (−2) ³
12 &equals; 7 ³ &plus; 10 ³ &plus; (−11) ³

Which of the numbers from 1-100 can be written as the sum of the cubes of three integers?

June 2019
MEI Conference 2019 - A couple of taster problems

The 2019 MEI Conference takes place at the University of Bath on 27-29 June. To see details of the conference and the wide variety of sessions on offer visit the conference website: conference.mei.org.uk

The following problems featured in the 2018 Conference sessions Using graphing technology for teaching calculus and Modelling and hypothesis testing with the Normal Distribution.

Which of the following is true:

Choose either adult men or adult women. How tall are the tallest and shortest that you are likely to meet? Use this to estimate mean and standard deviation.

May 2019
Calculator Crunch

Mathematics in Education and Industry contains the following number of letters in each word:
11, 2, 9, 3, 8.

Using just one pair of brackets, find the difference between the largest and smallest possible values of the expression:11 × 2 &plus; 9 ÷ 3 − 8

Calculators are allowed!

This is an example of the type of problem that will appear in Calculator Crunch: a new fun, free, summer challenge to help Year 6s get 'calculator-ready', and provide extra practice for Year 7s. For more details see mei.org.uk/Primary-KS2-3-Transition.

April 2019
April fool: 1=−1

Where is the flaw in the following argument?

March 2019
Regional differences

What is the maximum number of regions that two parabolas of the form y= ax ²+ bx+ c can split the plane into?

What is the maximum number of regions that three parabolas of this form, or four parabolas of this form, can split the plane into?

February 2019
Thinking equilaterally

Two equilateral triangles share a common vertex. Show that the lengths marked a and b are equal for any such arrangement.

Investigate the ratio a: b for other pairs of regular polygons.

January 2019
Happy 2019

Some problems about the number 2019:

The number 2019, its double 4038, and its triple 6057 contain all 10 digits. What is the next number with this property?

The number 2019 can be written as the sum of the first n perfect powers (integers of the form where a>0 and m≥2). What is the value of n?

2019 is the smallest number that can be written as the sum of the squares of 3 primes, p ²+q ²+r ², in n different ways (where the order doesn't matter). What is the value of n?

December 2018
Christmas trees

A Christmas tree is made by stacking successively smaller cones. The largest cone has a base of radius 1 unit and a height of 2 units. Each smaller cone has a radius 3/4 of the previous cone and a height 3/4 of the previous cone. Its base overlaps the previous cone, sitting at a height 3/4 of the way up the previous cone.

What are the dimensions of the smallest cone, by volume, that will contain the whole tree for any number of cones?

November 2018
Terms of engagement

The first three terms of the new sequence are 360, 756 and 1260. What is the fourth term?

Given that all the terms of the sequences are positive integers what could the original sequences be?

October 2018
Ritangle competition

Ritangle is a competition for teams of students of A level Mathematics, the International Baccalaureate and Scottish Highers: integralmaths.org/ritangle. The first five questions will be released on 1st, 8th, 15th, 22nd, 29th October 2018. Correct answers to these questions release a clue for the final question.
Question 1
How many 8 digit numbers are there that are both:
a) divisible by 18
and
b) such that every digit is a 1 or a 2 or a 3?
Question 2 Question 3 Question 4
In this question a and b are positive. A quadrilateral is formed by the points A, B, C and D where A is ( a,0), B is (0, b), C is (-1/ b,0) and D is (0,-1/ a). ABCD is always a trapezium.

If a=11 what value of b minimises the area of trapezium ABCD?
Question 5
Please don't share answers outside your team, others are having fun finding them!

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A list of Maths Items of the Month categorised by GCSE/A level topics can be seen at: Maths Items of the Month Curriculum mapping. M is the midpoint of the points of intersection of y= x 2 and y=2 x+ c (as c varies). Why does M move as it does?

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A magazine for the mathematically curious. Issue 11 now available: space-filling curves, cheating at cards and automated joke generation feature in our latest edition. Plus all your favourite puzzles & columns.

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Euclidea is all about building geometric constructions using straightedge and compass. About doing it the fun way. With Euclidea you don't need to think about cleanness or accuracy of your drawing - Euclidea will do it for you. But it's also a game. A game that values simplicity and mathematical beauty. Find the most elegant solution - the one, which is built in the least possible moves, - and you'll get the highest score.

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Euclidea is all about building geometric constructions using straightedge and compass. About doing it the fun way. With Euclidea you don't need to think about cleanness or accuracy of your drawing - Euclidea will do it for you. But it's also a game. A game that values simplicity and mathematical beauty.

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Due to Flash Player support being removed from browsers, our online evaluation resources are no longer available.
Each Primary Games Volume can be purchased to run on Windows based PC's.
These installable downloads do NOT require the Flash Player to run.

For over 20 years we have created a variety of CD and online primary school maths games and resources, resulting in 8 volumes of maths games. The contents of each volume can be viewed via the 'Primary Games' menu or the links below.

Many of the Primary Games have been redesigned as apps for tablets and phones.

Please visit our sister site:

All our online activities at www.primarygames.co.uk required Adobe Flash. Unfortunately, Flash support in browsers has come to an end. Fear not! You can still install the games to a Windows based PC, run them in full screen, without the need for an internet connection or the Adobe Flash Player. (We're working on Mac versions!)

Each Primary Games Volume is only:

£10+VAT (£12) for a Home/Single User Licence*
£50+VAT (£60) for a Whole School Site Licence*

*Indefinite Licence, no futher payment required. Supplied as a .MSI - Windows Only.
On receipt of your order you will be sent a unique download link. Please allow up to 4 hours for delivery.

School Order Form (PDF)

For tablets and phones, please see our sister site:

Times Tables Karate - Out Now!

Times Tables Karate - develop quick and accurate recall of times tables facts. Features include:

A two player duel :: Belt achievements - Earn a black Belt for recall of all facts to x12 :: Earn a Dan - Facts up to x25 :: Timed Training - A Year 4 Multiplication Check Emulator :: Download reports :: Print out achievement certificates

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Primary Games Volume Two :: Download and Install Primary Games Volume Two

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Due to Flash Player support being removed from browsers, our online evaluation resources are no longer available. Each Primary Games Volume can be purchased to run on Windows based PC's. These installable downloads do NOT require the Flash Player to run.

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Great origami for kids, and so fun to make…

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Practice Math Online with AI-Powered Alcumus | AoPS

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The best 100% free online math learning system, Alcumus uses adaptive AI to challenge high-performing math students with questions optimized to their abilities.

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Use logic to solve visual, interactive mathematical puzzles. Create your own puzzles to share with your friends or the SolveMe Community.

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The links below take you to a selection of short problems based on UKMT junior and intermediate mathematical challenge questions. You may wish to use them for practice, revision or a mathematical workout!

Longer NRICH problems can be found on the Topics in Secondary Mathematics page.

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Short Problems for Practice and Revision

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The links below take you to a selection of short problems based on UKMT junior and intermediate mathematical challenge questions. You may wish to use them for practice, revision or a mathematical workout! Longer NRICH problems can be found on the Topics in Secondary Mathematics page.

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Interactive Maths - The Interactive Way to Teach Mathematics

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Making use of the fantastic UKMT Individual Challenges, I have generated a page that randomly selects questions within specific parameters. You choose which age range you are aiming it at (Junior is...

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CEMC at Home has been developed to support teachers, students and parents during these challenging times. Most weekdays, we will post something for each of four grade levels: Grade 4 to 6, Grade 7/8, Grade 9/10 and Grade 11/12. The goal is to provide a wide variety of fun and educational ways to do mathematics and computer science while at home practicing social distancing. The resources will include games, new problems to solve, applications, videos, pointers to existing materials and more.

Subscribe Now!

Current Resources (March 26, 2020)

Our hope is that these resources make it to as many parents, teachers, and students as possible. Please help us achieve this by forwarding this information to your friends, family and colleagues. Share this information in person or electronically and let's get the conversations going! Many of the activities will encourage exploration and discussion and we hope that you share your thoughts with each other and stay connected.

Solutions and Archived Resources

Past resources can be found below as well as solutions to some problems.

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Design - Graphics, University of Waterloo

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CEMC at Home has been developed to support teachers, students and parents during these challenging times. Most weekdays, we will post something for each of four grade levels: Grade 4 to 6, Grade 7/8, Grade 9/10 and Grade 11/12.

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A home for curious mathematical minds. For ages 10-16 anywhere in the world. 100% free. Live interactive Maths Circles and puzzle sheets every week.

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Matt Parker has launched Matt Parker's Maths Puzzles! Once a week Matt will be making a puzzle video, in addition to his normal Stand-up Maths videos.

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A great collection of interactive mathematical problems and proofs.

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Interactive Mathematics Miscellany and Puzzles

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An encyclopedic collection of math resources for all grades. Arithmetic games, problems, puzzles, and articles

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Wild Maths - explore, imagine, experiment, create!

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Wild Maths is a collection of mathematical games, activities and stories, encouraging you to think creatively. We've picked out some of our favourites below - have a go at anything that catches your eye. If you want to explore games, challenges and investigations linked by some shared mathematical areas, click on the Pathways link in the top menu.

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A large collection of elegant mathematical problems and their solutions.

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Welcome to my selection of mathematical puzzles.

What's new? See puzzle 160.

The math puzzles presented here are selected for the deceptive simplicity of their statement, or the elegance of their solution. They range over geometry, probability, number theory, algebra, calculus, trigonometry, and logic. All require a certain ingenuity, but usually only pre-college math. Some puzzles are original.

Explaining how an answer is arrived at is more important than the answer itself. To this end, hints, answers, and fully worked solutions are provided, together with links to related mathematical topics. Further references are provided with many of the solutions. The puzzles are intended to be fun, with an educational element.

Each puzzle is assigned a level of difficulty of between one and four stars, with four being the most difficult. Clearly this is to some extent subjective, but it may be useful as a rough guide.

The source for each problem is given at the bottom of the solution page. I usually provide only a proximate credit; some math puzzles have been around for so long it can be difficult to trace their provenance. However, if I know the original source, such as when a puzzle is a recognized mathematical theorem, I credit that source.

I welcome feedback of any kind. Should you find a puzzle ambiguous, a hint misleading, an answer incorrect, or a solution unclear, please let me know. I also welcome new math puzzles.

Some brief biographical information. I gained a maths degree from a British university in the 1980s. I've worked in computer software since then, but I retain a keen interest in mathematics and in education.

Nick
Back to top
Nick Hobson
nickh@qbyte.org

Last updated: February 26, 2009

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Welcome to my selection of mathematical puzzles. What's new? See puzzle 160. The math puzzles presented here are selected for the deceptive simplicity of their statement, or the elegance of their solution. They range over geometry, probability, number theory, algebra, calculus, trigonometry, and logic. All require a certain ingenuity, but usually only pre-college math.

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Instead of funding these videos through sponsored ad reads at the end of each one, or separating out some behind a paywall, they're funded directly through viewer support.

If they add value to your life, it would mean a lot if you considered joining the supporting members. Benefits range from early access to new videos, to having your name in the video credits.

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Mathematics with a distinct visual perspective. Linear algebra, calculus, neural networks, topology, and more.

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An index of currently available Puzzles for Today, with the answers.

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Hey folk! Here are links to all of the #MathArtChallenge…challenges. :) Please feel free to share widely. This dropbox folder has lots of videos/pictures, too. Also, if you have an idea for a…

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Congratulations

You Have Won!

Start Again

BUST

You have gone over 23!

The Computer Wins

Start Again

The computer wins

Don't be discouraged, play against the computer to learn its strategies.

Start Again

Two players (or one player and the computer) take it in turns to move the lifesaver ring on to a number. This number is added to the running total for this game. The object of the game is to reach a total of 23. If a player makes the running total greater than 23 they have lost.

This game also works well with students playing in pairs at desks around the classroom. After each game the players move to a new desk, winners moving clockwise around the room and losers moving anticlockwise.

The game will need to be played a number of times by students before they start to see that there are some strategies that can be employed.

Note that each player has to move the lifesaver ring to a new number when it is their turn, they cannot stay on the number the lifesaver ring is on.

For the 1 player game above it is always possible to beat the computer as the player always has first move.

The strategy used by the computer to play this game is explained here when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher, tutor or parent you can apply for one here.

A Transum subscription also gives you access to the 'Class Admin' student management system, many more teaching resources and opens up ad-free access to the Transum website for you and your pupils.

There is a printable worksheet to go with this activity.

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A game involving mental arithmetic and strategy for two players or one player against the computer.

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If you see a network or MIME error, try another port (stop other dev servers), hard refresh, or run from the project root after npm install.

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A game requiring you to devise a strategy far more complex than that required for the standard noughts and crosses game.